Includes bibliographical references (p. [479]-499) and indexes.

Introduction.- Basic Material.- Basic Material: Kahler Manifolds.- Relativity.- Riemannian Functionals.- Ricci Curvature as a Partial Differential Equation.- Einstein Manifolds and Topology.- Homogeneous Riemannian Manifolds.- Compact Homogeneous Kahler Manifolds.- Riemannian Submersions.- Holonomy Groups.- Kahler-Einstein Metrics and the Calabi Conjecture.- The Moduli Space of Einstein Structures.- Self-Duality.- Quaternion-Kahler-Manifolds.- A Report on the Non-Compact Case.- Generalizations of the Einstein Condition.- Appendix. Sobolev Spaces and Elliptic Operators.- Addendum.- Bibliography.- Notation Index.- Subject Index.

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. Einstein Manifolds is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.